# Math Help - What does notation max{ a : b } means?

1. ## What does notation max{ a : b } means?

I dont know where to post this question. In information theory Capacity C = max{I(Xk;Yk) : E[Xk^2]=P} where maximization is wrt probability fx prob. density fn of Xk. What does this value C equals? Can anyone explain that notation. -Devanand T

2. ## Re: What does notation max{ a : b } means?

The curly braces seem to be the set-builder notation,

3. ## Re: What does notation max{ a : b } means?

max{ a : b } means it return you a max value in a , b

max (10,9) = 10

max(2,9) = 9

4. ## Re: What does notation max{ a : b } means?

Originally Posted by Neeraj
max{ a : b } means it return you a max value in a , b

max (10,9) = 10

max(2,9) = 9
Can you explain why you think that this interpretation is more likely than the one in post #2?

5. ## Re: What does notation max{ a : b } means?

Originally Posted by dexterdev
I dont know where to post this question. In information theory Capacity C = max{I(Xk;Yk) : E[Xk^2]=P} where maximization is wrt probability fx prob. density fn of Xk. What does this value C equals? Can anyone explain that notation. -Devanand T
My best guess is this: maximize the mutual information between Xk and Yk, subject to the constraint that the expected value of Xk^2 is P.

As far as I know (I don't know much about channel capacity), the part about the expected value of Xk^2 is not part of the standard definition of channel capacity. See, for example, Channel capacity - Wikipedia, the free encyclopedia